ADVANCED: Randomization

GVPT399F: Power, Politics, and Data

Randomization

  • Last session, we randomly assigned 1,000 hypothetical people to two different groups

  • Testing whether randomization helps us create two roughly identical groups prior to treatment

  • You now have a lot of the R code needed to replicate that analysis

Creating our group of 1,000 people

Imagine we have a group of 1,000 individuals. We know the following about them:

  • Height

  • Weight

  • Eye colour

Creating our group of 1,000 people

group_df <- tibble(
  id = 1:1000,
  height = rnorm(1000, 170, 6),
  weight = rnorm(1000, 80, 10),
  eye_colour = sample(c("Blue", "Green", "Brown", "Grey"), 
                      1000, 
                      replace = T)
)

group_df
# A tibble: 1,000 × 4
      id height weight eye_colour
   <int>  <dbl>  <dbl> <chr>     
 1     1   174.   98.8 Grey      
 2     2   164.  100.  Brown     
 3     3   169.   79.7 Blue      
 4     4   181.   95.7 Brown     
 5     5   168.   69.0 Grey      
 6     6   176.   89.5 Blue      
 7     7   172.   78.6 Brown     
 8     8   165.   96.4 Grey      
 9     9   168.   83.5 Green     
10    10   167.   89.2 Green     
# ℹ 990 more rows

The Normal distribution

ggplot() + 
  geom_density(aes(x = rnorm(n = 1e6, mean = 0, sd = 1))) + 
  theme_minimal()

Random sampling from the Normal distribution

I can take a random sample of n values from a Normal distribution centered at some mean with a specific standard deviation.

  • By default, rnorm() takes a mean of 0 and a standard deviation of 1

  • The following code takes 1,000 random samples from that default Normal distribution

Random sampling from the Normal distribution

rnorm(n = 1000, mean = 0, sd = 1)
   [1] -0.4836451284 -1.1875016746  0.0951045573  0.4161549287  0.3328495027
   [6] -0.3675878935 -0.4509144921 -1.1274279907  0.1597328249  0.5679996301
  [11]  0.9364744797 -0.4283838637  1.2412014214 -0.9939471216  1.5445143862
  [16]  0.4580566709  0.2136140195 -0.7574498184  1.5934207630 -0.4983762266
  [21] -0.5186502849  1.0340094675  2.1085428770 -0.2699352157 -0.2004133641
  [26] -1.0890308688  0.2003922172  0.4516307832 -0.7283713394 -0.8658711114
  [31]  0.2532793296 -0.9108621138  0.5581557738  0.5308943982  0.6836507234
  [36]  0.4022824831 -0.1481263195  1.0118899290 -1.5643658496  0.6591029061
  [41]  0.6033318284  1.3590540928 -1.9185935281 -0.2875171421 -0.6479373075
  [46] -0.5807785416 -0.4247936897 -1.2657025482 -1.5375823099 -0.7689679269
  [51]  1.7177754538  2.3855579442 -0.4082832760  0.1964898204  0.6187416065
  [56] -1.5410842090  0.2483364199  0.8690090792 -1.0830629440 -1.6344641066
  [61] -1.3118246178  1.0226187927  0.6950671918  0.7917783230  0.5831438751
  [66]  1.1111556485 -0.3464610560 -0.9367118747 -1.6469062870  0.3244974162
  [71] -0.0581087680 -1.7056350884 -0.4396285030  1.2387185409  0.8205139484
  [76] -0.4370778374 -1.3214397685  1.2696981452  0.0303614381  0.7065415605
  [81] -1.1925087158 -0.4970581551  0.9190863157  0.1145800558 -2.1909181705
  [86]  0.4404761754  0.8423455466  0.0621534381 -0.0989780473 -0.7650508667
  [91] -0.1439972053  0.8885925431  0.3928929892 -1.2251976629  1.0342379752
  [96]  1.6987835770 -0.6073597166 -1.4421677479 -1.0791762590 -0.4123765884
 [101] -0.4591838325 -1.0373763009 -0.4754937114  1.3601876797 -0.9896644000
 [106]  0.0129438339 -1.1780024829 -0.8833722863  0.3125069213 -1.2583469373
 [111]  0.3238550953  1.3656489206 -0.0472093730 -1.0352423708  1.5315147637
 [116]  0.0196529989 -0.0044640397  0.6781645371  0.3518304581 -0.5740819166
 [121] -1.6683242187  0.3548239255 -1.8847520249 -0.6826181796 -1.2881851775
 [126] -0.6758324094  0.7951817035  0.0771914803 -0.7948461695  0.1870475275
 [131]  0.6874257360 -0.2909559182 -0.0600399209 -0.8037700972  0.2249030363
 [136] -0.7208769138 -1.1677952857 -0.1195635555 -0.7971127419  0.5677172220
 [141]  0.0955852275  0.0343873045  1.5183850002  0.0400987703  0.7947023290
 [146]  1.3916775379  1.1083727663  0.0393155394 -0.9207806766  1.6161471199
 [151] -0.8713687850 -1.3706631636  0.2359460744 -0.0576167258 -0.3275287803
 [156] -0.4715108053  0.0706226868  0.4299868464  0.8654012840 -0.1124527391
 [161] -0.1019562494  0.6265535017  1.6829455126 -0.1383225394  0.0163471831
 [166]  0.9699962833 -0.3161965426 -0.7817225475  0.2605148299 -1.0895071207
 [171]  0.9976295481 -1.2440701971 -0.1846587114  0.5671999088 -0.4249912480
 [176]  1.7321818646  1.4846911751 -0.5502417321 -1.0054025257 -0.6924746591
 [181] -0.0063669066 -0.0782895449 -1.2129655845 -0.1502467363  0.5771505418
 [186]  0.7068701536  1.8292523721  1.9232444541 -0.2157256988  0.9253611711
 [191]  0.4901944459 -0.9007551531  0.3079666859  1.2461198788 -0.4803876625
 [196]  1.1233508245  0.6253697609 -1.3777572842 -0.5200273991 -0.2193945292
 [201] -0.3475052833 -0.9303135311 -1.0343636189 -1.0830539505  0.8272758257
 [206]  0.2038390484  0.5109036215 -0.9839433266 -2.2210004906  1.3373192206
 [211] -2.0918966281  1.2185871443 -1.1846135479 -0.7206535179 -0.3728147593
 [216]  2.0556150147  0.9177497659 -1.9760274700 -0.1616319842 -0.3826807170
 [221] -1.4662604617 -0.8986258798 -0.4746366495  0.4929364077  0.6894052026
 [226]  0.8388444799 -0.6043303241  1.2154495802  0.3006407549 -0.3039686455
 [231] -0.4603054884 -0.4250138396 -0.0877408840  1.0373074304 -0.3471094170
 [236] -1.4909752268  0.2101903214 -0.3417390323  2.1050593659  0.0184417710
 [241]  0.7739804258 -0.2256468772 -0.0257634183  0.1618171280 -1.0122270156
 [246]  1.2148287406  0.3777065890 -2.6237943375  1.2505335950 -0.6563333904
 [251]  0.6646474347 -0.3183409210 -1.0056581389  0.1734635075  0.0659844037
 [256]  0.6066900143  0.4779301565  0.5281309920  1.2579772902 -0.0305853253
 [261] -0.2883627775  0.4152819298  0.8208750038 -0.3122607003  0.7609194340
 [266] -0.6412704454  1.0515624875 -0.3651170347 -0.1824580713  1.5924319705
 [271]  0.9581938442 -0.6239716660 -0.7607264320  0.4725513137  0.5920006007
 [276] -1.1820373479 -0.7514382703  0.3989569581  1.0801518590  0.0296265937
 [281] -0.1771940431  0.7581294393 -0.0188590324  1.4523262545 -0.4983730047
 [286] -2.0376598934 -0.5813354338 -0.5637605129 -1.0204262901  0.6336455856
 [291] -0.8577227079  0.0210450051 -0.7749635484 -0.4812368771  0.6080950817
 [296] -0.8656521774  0.0140657427 -0.3356300783 -1.0820253738  0.1551770217
 [301] -0.3833048843  0.2164632838  0.2566119056 -1.2855215328  1.2120197394
 [306] -0.5837567758 -1.6079337137 -0.7313134272  1.6654847009  0.7816741280
 [311]  1.0163824944 -1.3833770466 -1.1653157078 -0.6896260283 -2.6445812458
 [316]  0.3403727931  0.2409589277 -0.2311685624  0.3228886388 -1.2562520849
 [321] -0.2225718538  0.5185379148 -0.2624171374  0.8553388907 -0.9834422432
 [326] -0.7077338638  1.1387930839 -1.7144612827  0.9072146731  1.4310489203
 [331] -0.5488465899  0.0709981924 -1.6839782697  0.9674834761  1.4346327776
 [336] -0.2619739299  1.1157090228 -0.0042254649  0.7650301843  2.1340107309
 [341]  0.8788756147  0.1316290191  1.0116584755 -0.1342490843 -1.5249120935
 [346] -0.6905857717 -0.6600110392  0.5880787402 -0.0274150156 -0.0710808610
 [351] -0.0986633077  0.4986809254  1.5233759875  2.4451641859  0.4496482710
 [356]  1.0813384162  0.8339131867 -1.3497065167 -0.4596678774  0.5300017091
 [361] -0.7771846066  0.0194369733  0.1340086492  0.1246425878  1.7748373533
 [366]  1.5274385412  1.1426093412 -0.4403314561 -0.2283576366 -1.3484890496
 [371] -2.8024620859  1.1058829137 -1.0548799363  0.5936777723  2.2481724186
 [376] -0.2825422436  0.8816549689 -0.0715651035  2.2361904854 -0.7037769165
 [381]  0.7489208264 -0.6926999160 -0.8965405439 -0.2359817884  0.6329210804
 [386]  1.3818323843 -0.1316868431 -0.5728862859 -0.3739536891 -1.4661426714
 [391] -0.1817818596 -0.3163288877 -2.8786965141 -1.7125531162 -0.3833544671
 [396]  0.3433732321  0.9412928209  1.7941204814 -0.9774724919  0.6965818802
 [401] -0.6089072386 -0.0076092687 -1.9726137172  0.2214561428  0.2414638455
 [406]  1.1004697918 -0.1604738533 -1.2986925341 -1.2792521553  1.6479340409
 [411]  1.4341359819  0.1075277678  0.3188324037  1.1764411518 -0.7288897251
 [416]  0.7019610457 -0.6392895032 -0.9639199448  0.1086377867  1.9407510816
 [421]  0.0717152305 -0.5877385574 -0.7891048535  0.1382771592 -1.1064906980
 [426]  1.4079935382  0.9758748481  0.7271617504  0.2406844802  0.6540486352
 [431]  1.0575216281 -1.5207990827  1.2606045932  0.3723856293 -0.3871113035
 [436] -0.7022061557  0.9887859089  0.6212126961  0.5253981581  1.4515458614
 [441] -0.2322636741  0.9277354227  0.6174960747  0.6782526691  0.1696357464
 [446]  0.5901631976  1.1993720735 -1.4850209442  1.2690277411  0.3496930192
 [451]  0.3052142267 -0.8536583267 -1.7614857343 -1.5796579288  0.1109311755
 [456] -0.9354909167 -0.4721844555  1.1222686206  0.9571213179 -0.7585717264
 [461] -0.2315139150 -0.0246307780 -0.3353867743  0.1572460558 -0.1950751632
 [466]  2.1102497877  0.1568761267  0.0121177134  0.7344195712  1.0145952321
 [471] -0.4392486867  1.3087664724  3.0376701753 -0.5095984071 -1.0470678793
 [476]  0.9127153444 -0.5760297082 -1.3324262273 -0.3901971930  0.0444281392
 [481] -0.3141201594 -0.1533380131 -1.3507026732  0.3105442979  1.9904187456
 [486]  0.7387973068 -0.7238224877 -0.1339562274 -0.4485584092  0.6522423720
 [491] -1.4094703391  1.5154569283 -0.2048373034  0.8638308348  0.2036166267
 [496]  0.3111864717  0.3149124046 -0.4852932240  0.9134950520  0.6160283931
 [501] -0.8432962637  1.0395001094 -0.1807690636  0.1815932298 -0.0364674047
 [506] -1.5457769908 -0.7224609909 -0.4101124485 -0.0712471149  0.2133816801
 [511]  0.1467953609 -0.3660024293  1.7096005090  0.1793314625 -1.1848746847
 [516]  0.9566659513 -0.2848614748 -0.5174009148  0.9513638701  1.2491369189
 [521]  1.4576833709 -0.5959326439  0.6578966502  1.5329596527 -1.2923003105
 [526]  0.0006966424  0.4628438404  0.7389971283 -0.1019795127 -0.6251025855
 [531]  2.1683522454 -0.4379636880 -0.2503422016 -1.6503803362 -1.7791830740
 [536]  0.9646212797  1.3305892780 -1.5371497444 -1.1921674168  0.6402878634
 [541]  0.1786929976  0.9098440396 -0.5023860178  1.7449988653  0.3331418903
 [546]  1.0203578644  0.1631673546  0.6309882636  0.4259357610  0.0548613137
 [551] -1.3541611907 -0.6700048531  0.0377089718  0.7491862607 -0.5241392066
 [556]  0.7252292142  0.0251038473  0.9043346452  0.3815080086 -0.8069029934
 [561]  0.8267859394 -0.5025565667 -1.4021960894 -0.3696379145  1.1451386425
 [566]  0.3318346168  0.6817699957  0.2226076429  0.1341867089 -0.6696571929
 [571]  1.6600492599 -0.7011061782  0.5603543203 -0.7396321781 -0.7505906897
 [576] -0.5894255644  0.8832112434 -0.0641040635 -0.2176308190  0.8746215097
 [581]  1.4796041357  1.4990856549 -1.5744105019  0.9384009969 -1.8049299965
 [586] -1.0031613145  0.4280213976 -0.9221967419  0.7643272832  1.2590507773
 [591]  0.3230497472 -0.2072091034  1.0077720168 -0.6196428589  2.1242423235
 [596]  0.8158472307 -0.1133093990  0.3108222460  0.0718293248  1.1384512102
 [601]  1.6886276347 -0.2450787223 -1.3472731632  0.6730120902 -1.2763956988
 [606]  2.1576304012  0.6866677200  0.0530922814  0.7924787547 -0.9877625617
 [611] -1.0693316404  1.0125116540  1.1915987729  0.4941178384 -1.0922409162
 [616]  0.8018722413  1.0673541735  1.4869661032  1.2211756124 -0.8692541220
 [621] -0.8065158169 -0.4704433005 -0.5517453216  0.5045492184  0.0343119078
 [626]  0.9310748563 -0.2498176177 -1.5973085667 -0.7681771260 -0.4616576541
 [631] -1.0309805853 -0.3742246601  0.1877278960 -0.8289697596  0.2163702928
 [636] -0.5216680802 -0.8398894166  0.9069275694 -0.9251493114  0.7473277751
 [641] -1.1754401290  0.4394214813  0.3114223133 -1.5753615042  2.9859089006
 [646] -0.0656091631  0.7247194388 -0.5768706558  0.4251927422  1.6281566146
 [651] -0.5317206359 -0.6621995731  0.5156416093 -0.8990189980  1.7024947442
 [656]  0.6611493060  0.6414009238 -0.6765078585  0.1466760432 -0.8718944614
 [661]  0.0225531696  0.3875557493 -0.6738770475  0.5683926611 -0.7955691112
 [666] -0.7959819257  0.2206262083 -0.6663271640 -1.4994914986  0.4952163837
 [671]  0.4311670177 -0.4213886224  0.6144711905  0.5372197194  0.1685562556
 [676]  1.9069029232  0.8100612166 -0.2841184833  0.1154602441  0.4242384646
 [681] -1.5060957206  0.2697100827  0.7795280439 -1.3373320912 -0.8649932128
 [686]  0.4299730854 -0.9840737414 -0.7935270674 -0.5448715905 -0.0291942179
 [691] -0.4878378584 -0.4029204960  0.9761663642 -0.3965432783  0.4579208222
 [696]  0.7994075011 -0.1985215249 -0.3057812146 -0.0549613621  1.4435408748
 [701] -0.0191456655 -0.6744189910  0.9990566000  0.1980711121 -0.1702279066
 [706]  1.5823995521  0.3412561057 -2.6603812930 -0.1596922289 -1.6580872462
 [711]  0.0689178393 -1.6883497166  1.1081357033 -1.0927995715 -0.5078441154
 [716]  2.1325323387  1.5499973824 -0.2016353281  0.7077832822  2.0204803837
 [721]  0.4848801686 -0.1218917585 -1.8920910211 -1.3247965766  1.9579757676
 [726]  0.4061649447  0.2801171485 -0.5845486952  0.4563146806  2.1973808316
 [731]  1.0303694679  0.4780569951  0.1537514595  1.6711719936 -1.0474424782
 [736] -0.4268205582 -0.3006919079  0.2292576317  2.0049756564 -2.0518024737
 [741]  0.7383687936  0.7921716881  0.1638961922 -0.3693159812 -0.3079452133
 [746] -0.4499103930  0.2305509863 -0.3761491603  0.7450946403  0.8677312832
 [751] -0.3423780593  0.3703922021  0.5867472480 -0.4102302939 -0.8515286913
 [756] -0.1210821347 -0.4301611532  0.0694036676  1.4113289412  0.4062385625
 [761]  0.1041548681  0.3654351899 -0.0526087542 -0.0998145511  0.7370502134
 [766]  0.0912183994  1.1052045358 -1.6195314801  0.3207859765  1.3926498193
 [771] -1.9671422296  0.5065659980  0.2620163060  2.4302878531 -0.5513493943
 [776] -0.3180170038 -0.2058682537 -0.7339024515 -0.9123086609  0.3260453392
 [781] -1.2402301373  0.8629326578 -0.5176458788  0.6572623833 -0.6849035717
 [786]  0.5542060144 -0.8028483155 -1.7352078468 -0.4197565847  0.5240366522
 [791]  0.1463990201 -1.3648726875 -1.6990220309  3.1599484192  1.8669566298
 [796]  0.0747971169  1.3510108444  0.2958213463  0.0133698907 -1.9771332527
 [801]  0.1545071273  1.6306038036 -0.3759082200 -0.4263711495 -1.2482388527
 [806] -0.0139393755  0.8058816089 -0.6056462996 -0.4499170082 -1.8003631162
 [811] -0.3358125673  1.7673225388 -1.5857667770  0.4262468387  0.6016917207
 [816] -2.0382006968 -1.0535266578  2.2820124887  0.6313760439 -0.3420761388
 [821]  0.2989175010 -0.1909381340 -0.1311342968  0.0387505486  0.1818408637
 [826] -0.0491542204 -0.9218950206  0.0036253002  0.4564509054 -1.2863338436
 [831] -1.9435420934  1.2784555610  0.2407167455 -2.0336172978 -0.5926652869
 [836] -1.0941104899 -1.0019330711 -0.2654872226 -1.1529195355 -2.0753614254
 [841]  1.3543763684  0.5287371625 -0.5079018654  0.1461869450  0.0672803198
 [846]  2.2090958318 -0.7316932101  0.5539233564 -3.2387717714  1.4058302556
 [851]  0.1157947890  0.1245588175  0.0162330544 -0.6356524978  0.9627977985
 [856] -0.6550247137  1.7483058010 -0.2437150265  1.4461489822  0.7104849690
 [861]  0.9695699991 -0.3428630311 -0.8587043961 -0.0710076589 -0.6996424177
 [866] -2.5763677348 -0.2813752943 -0.6551756059  0.5357262657 -0.6709851758
 [871]  0.3828331612 -1.8101741643  0.1642250624 -0.6412370253  0.3954362457
 [876]  1.1197368933  0.2889744610 -1.0458520625  0.9930929401 -0.5346275237
 [881] -0.8495895050 -0.1253190110  0.2251887255 -0.8542893309  1.1467475414
 [886] -0.2093908859 -1.1246637451 -0.6122374776  0.4821463440 -0.5453693923
 [891] -0.8556947850  1.4110082413  1.0231438594  0.2321484859 -0.8913605358
 [896]  0.3105589389  0.7188640419 -0.6961468397 -0.1832333286  0.4620892503
 [901] -0.3867333686  0.0762175269 -0.9460784534 -0.6618119619  1.6541997530
 [906] -1.5630615504 -0.9941363851 -1.8973367415  0.4572378893 -2.0722466884
 [911] -0.3142923878 -1.6491651144  0.8330944140  0.6384892208 -1.8209987262
 [916]  0.4017384194  1.2320533569  0.4598113596  0.0919276555 -0.3043272228
 [921]  0.3543627401 -0.4423864814 -1.2484624198  0.0840478279  1.2564178493
 [926] -0.7287802376  0.2902808584 -1.1750437218  1.3041150103 -0.1718257385
 [931]  0.9248447587  0.5220837991 -0.6248146786 -1.0832569236 -1.4416310069
 [936] -0.3113088815  1.0653771319  0.6481543102  0.1205755552  0.1062149140
 [941] -1.0335037332 -0.1897882927 -1.1961599338 -0.2252520932 -1.1287905910
 [946] -0.1964761555 -0.7000179679  1.0019025483 -0.9036488431 -1.7216750291
 [951] -0.6691164914  0.1309922322 -1.2751952659  2.1899066313  1.5179062260
 [956] -2.5659491437  0.7254199873 -0.7512737205  0.6466112855  0.1109314644
 [961] -0.5572302704  0.9574127782 -0.9623048583  0.9776375319  1.1906903794
 [966] -1.1379532412  0.0897794013 -0.5359172323 -0.7991755900 -0.6125497717
 [971] -0.8016627125 -1.6315584441 -0.3112163631 -0.1433825547 -0.7463813938
 [976]  0.9247069583  0.9650676304 -1.1708322241 -0.3677954719  0.6552518739
 [981] -0.7883818098  0.0153124574 -2.3399583574 -0.6401073543 -0.7546975184
 [986] -0.2374098133  1.9712426840 -0.9196433327  0.8960800671  2.0057042762
 [991]  0.9753223350  1.5840126581 -0.4054775333 -0.0899474407  1.2273041669
 [996]  0.2745560707 -0.5610143409  0.2205999792 -0.5780430751 -0.7536004661

Random assignment using the Binomial Distribution

Remember, we then randomly assigned them to one of two groups: A or B.

  • I used random draws from the Binomial (read: binary or two) distribution to do this.

Random assignment using the Binomial Distribution

rbinom(n = 1000, size = 1, prob = 0.5)
   [1] 1 0 0 1 0 0 1 0 1 1 0 0 0 0 0 1 0 1 1 0 0 1 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1
  [38] 0 1 1 0 0 0 0 0 0 1 1 0 1 1 1 0 0 1 1 1 0 0 1 0 0 1 1 1 1 1 1 0 1 0 0 0 0
  [75] 1 1 1 0 1 0 0 0 0 1 1 0 1 0 1 1 0 1 0 0 0 0 0 1 0 0 1 1 1 0 1 1 1 1 1 0 0
 [112] 0 1 1 0 1 0 0 0 1 1 0 0 1 0 1 0 0 1 0 1 0 1 1 0 1 0 1 1 1 0 0 1 0 1 1 1 0
 [149] 1 0 0 0 1 1 1 1 1 1 1 0 0 1 1 1 0 0 0 1 1 0 1 0 1 0 1 1 0 0 1 1 1 1 1 0 0
 [186] 0 0 1 1 1 1 1 0 0 1 1 1 0 0 1 0 0 1 0 1 1 0 1 0 0 0 1 0 1 0 1 0 1 1 1 1 1
 [223] 1 1 0 1 1 1 0 1 0 0 1 1 0 1 0 1 1 0 0 1 1 1 0 0 0 0 1 0 1 0 0 0 1 1 1 0 0
 [260] 1 1 1 1 1 1 0 0 1 1 0 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 0 0 0 1 0 1 1 1 0 0
 [297] 0 0 0 0 0 1 0 1 1 0 1 1 0 1 0 1 1 0 1 1 1 1 0 0 1 1 0 0 0 0 1 0 1 0 1 0 1
 [334] 0 1 0 1 0 1 1 1 1 1 1 0 0 0 0 0 1 0 0 1 0 0 0 1 0 1 1 1 0 1 1 1 0 0 0 1 0
 [371] 0 0 1 0 1 1 0 0 1 0 1 0 0 0 0 0 0 1 1 0 1 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1
 [408] 1 0 1 0 0 1 1 1 1 1 1 1 0 0 0 0 0 0 1 0 0 1 1 1 0 0 0 0 1 1 0 1 1 1 1 1 1
 [445] 0 1 0 0 0 0 1 0 1 0 0 0 0 1 1 0 0 1 0 1 0 0 1 1 0 1 1 1 1 1 1 0 0 1 0 0 1
 [482] 1 0 1 0 1 0 0 0 0 1 0 1 1 0 0 1 1 1 1 1 1 1 0 0 1 0 1 0 0 1 0 0 1 1 0 0 0
 [519] 0 1 1 1 0 1 1 1 0 0 1 1 0 1 1 1 1 0 1 0 1 1 1 1 1 1 1 0 0 0 1 1 0 0 1 1 0
 [556] 0 0 0 0 1 0 0 1 1 1 1 0 1 0 0 1 0 1 1 1 0 1 1 1 1 0 0 1 1 0 1 1 1 0 0 1 0
 [593] 0 0 1 0 0 1 1 1 0 1 0 0 0 0 0 0 1 0 0 1 0 1 0 0 1 1 1 0 1 0 0 1 1 1 1 1 1
 [630] 0 1 0 0 1 0 1 0 1 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 1 1 1 0 0 0 1 1 1 0 1 1 0
 [667] 1 1 1 1 1 0 0 0 1 0 0 1 0 1 1 0 0 0 1 1 0 0 1 1 0 0 1 1 1 0 0 1 0 0 0 0 1
 [704] 1 0 0 1 0 1 1 1 0 1 0 0 0 0 0 1 0 1 0 0 0 0 0 1 1 1 0 1 0 0 0 0 1 0 0 0 1
 [741] 1 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 1 0 1 1 1 0 0 1 1 1 1 0 0 1 0 0 1 0 0 1 0
 [778] 0 1 0 1 1 0 0 0 0 1 1 0 0 0 1 0 0 0 1 0 1 1 1 0 0 1 1 0 1 0 1 1 0 0 0 0 0
 [815] 0 1 0 0 1 1 1 1 1 1 1 1 0 0 0 1 1 1 0 0 1 0 0 1 0 1 0 0 0 1 1 0 0 1 0 0 0
 [852] 0 1 0 0 0 1 1 0 1 0 0 1 1 1 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 0 1 0 0
 [889] 0 1 0 0 1 1 1 1 1 1 0 0 0 0 1 1 0 0 1 1 1 0 0 1 1 0 1 0 0 0 0 0 0 1 0 0 0
 [926] 1 0 1 1 1 1 1 0 0 0 0 1 1 0 0 1 1 0 1 1 0 1 1 0 1 1 1 1 1 0 0 0 0 1 1 1 0
 [963] 0 0 0 1 0 1 0 0 1 0 0 1 1 0 1 1 1 1 1 1 1 0 0 1 0 0 0 0 1 0 0 0 0 1 1 1 0
[1000] 1

The Binomial Distribution

ggplot() + 
  geom_bar(aes(x = rbinom(n = 1e6, size = 1, prob = 0.5))) + 
  theme_minimal()

Assigning our people with mutate()

assigned_group <- group_df |> 
  mutate(
    group = rbinom(1000, 1, 0.5),
    group = factor(group, labels = c("A", "B"))
  )

assigned_group
# A tibble: 1,000 × 5
      id height weight eye_colour group
   <int>  <dbl>  <dbl> <chr>      <fct>
 1     1   174.   98.8 Grey       A    
 2     2   164.  100.  Brown      B    
 3     3   169.   79.7 Blue       A    
 4     4   181.   95.7 Brown      B    
 5     5   168.   69.0 Grey       A    
 6     6   176.   89.5 Blue       A    
 7     7   172.   78.6 Brown      B    
 8     8   165.   96.4 Grey       B    
 9     9   168.   83.5 Green      A    
10    10   167.   89.2 Green      B    
# ℹ 990 more rows

Comparing our two groups

Comparing our two groups

Comparing our two groups